1. Field of the Invention
The present invention relates to a method of simulating deformation of a rubber material which comprises: a filler part made of at least one filler particle; and a rubber part made of rubber and surrounding the filler part, with good accuracy.
2. Description of the Related Art
The rubber material is widely used in for example, tires and industrial goods such as sporting goods. To reduce the trouble and the cost of experimental manufacture, a simulation of for example, deformation process of the rubber material is carried out using a computer. The conventional simulation methods of the rubber material are described in for example, the following articles.
(1) “A THREE-DIMENSIONAL CONSTITUTIVE MODEL FOR THE LARGE STRETCH BEHAVIOR OF RUBBER ELASTIC MATERIALS” by Ellen M. Arruda and Marry C. Boyce, Journal of the Mechanics and Physics of Solids Volume 41, Issue 2, Pages 389-412 (February 1993).
(2) “CONSTITUTIVE MODELING OF THE LARGE STRAIN TIME-DEPENDENT BEHAVIOR OF ELASTOMERS” by J. S. BERGSTROM and M. C. BOYCE, Journal of the Mechanics and Physics of Solids Volume 46, No.5 PP. 931-954 (1998)
The article (1) describes a method for analyzing a rubber material using a molecular chain network model theory. According to the method described in this article, however, strain-rate dependence of general rubber material can not be replicated.
The strain-rate dependence is a characteristic of a rubber material showing different viscoelasticity characteristics depending upon its strain rate. That is, when amplitude strains of different frequencies (e.g., 10 Hz and 1,000 Hz) are applied to the same rubber test pieces, energy losses of the respective frequencies have different values. In the article (1), such the strain-rate dependence is not taken into consideration. Thus, material characteristics of different frequencies can not be evaluated precisely from one rubber material model.
Here, a pneumatic tire is used as an example of a rubber product, and two performances, i.e., its fuel efficiency and grip performance (index of stick of the tire with respect to a road surface at the time of acceleration and/or deceleration) will be considered. First, in order to enhance the fuel efficiency of the tire, it is effective to use a rubber having small energy loss for a tread rubber when a vehicle runs at general steady running speed. That is, when the fuel efficiency is to be evaluated, it is necessary to check the energy loss of rubber at a low strain rate of about from 10 to 100 Hz at frequency.
On the other hand, in order to enhance the grip performance, it is necessary to use a deformable rubber for a tread rubber such that the rubber fits to fine projections and depressions on a road surface at the instant when the rubber comes into contact with the road surface. For this purpose, in order to enhance the grip performance, it is desirable that the rubber has high energy loss at the time of high speed deformation. When evaluating the grip performance, it is necessary to check the energy loss of rubber at high strain rate of about from 10,000 to 1,000,000 Hz at frequency.
FIG. 21 is a graph showing a relationship between the frequency of strain rate and the energy loss calculated using frequency-temperature conversion rule with respect to a tire rubber material, and the relationship is shown with solid line. As apparent from the drawing, if frequency is varied, the energy loss is also largely varied. According to the method of the article (1), however, even if the strain rate of the rubber model is changed, only the same energy loss is obtained as shown with chain double-dashed line. With this, data useful for developing rubber can not be obtained. The strain rate is a product of deformation frequency and strain.
The article (2) describes that a rubber model is set from rubber material in which a filler is mixed, and the strain-rate dependence is taken into consideration. When deformation of the rubber material is calculated, the handling of an interface between the filler and rubber is important problem. As a result of various researches, it was found that in the interface, relatively high energy loss was generated due to slip or friction between the rubber and filler. Therefore, in order to carry out a precise simulation of rubber material, it is important to model the filler and the rubber separately.
According to the technique described in the article (2), however, the filler and the rubber are modeled collectively not separately. With such a method, it is not impossible to obtain information such as a state of interface between rubber and filler and a distribution state of stress at the time of deformation.